# Labor Supply Mechanism Tests

| Model | Dep Var | N | Countries | R² |
|---|---|---|---|---|
| C1: Z → LFP | lfp_rate | 5,868 | 175 | -0.029 |
| C2: LFP → log(REER) | log_reer_combined | 3,092 | 95 | 0.002 |
| C3: Z → log(REER) (no LFP) | log_reer_combined | 3,222 | 99 | 0.024 |
| C4: Z → log(REER) + LFP | log_reer_combined | 3,092 | 95 | 0.023 |
| C5: Z → GDP growth | rgdp_growth | 5,466 | 171 | 0.015 |
| C6: Z → log(REER) (no growth) | log_reer_combined | 3,235 | 99 | 0.022 |
| C7: Z + working_age_share | log_reer_combined | 3,222 | 99 | 0.025 |

## Key Coefficients

| Model | Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|---|
| C1: Z → LFP | Z_1 | -3.2628 | 4.0865 | 0.4247 |  |
| C1: Z → LFP | Z_2 | 0.2349 | 0.6079 | 0.6992 |  |
| C1: Z → LFP | Z_3 | -0.0025 | 0.0251 | 0.9206 |  |
| C1: Z → LFP | log_gdp_pc | 0.8572 | 0.2424 | 0.0004 | *** |
| C1: Z → LFP | rgdp_growth | 0.0081 | 0.0021 | 0.0001 | *** |
| C2: LFP → log(REER) | lfp_rate | 0.0009 | 0.0010 | 0.3317 |  |
| C2: LFP → log(REER) | log_gdp_pc | 0.0066 | 0.0096 | 0.4943 |  |
| C2: LFP → log(REER) | rgdp_growth | -0.0001 | 0.0003 | 0.7756 |  |
| C3: Z → log(REER) (no LFP) | Z_1 | -1.2092 | 0.3759 | 0.0013 | *** |
| C3: Z → log(REER) (no LFP) | Z_2 | 0.1551 | 0.0544 | 0.0044 | *** |
| C3: Z → log(REER) (no LFP) | Z_3 | -0.0057 | 0.0022 | 0.0088 | *** |
| C3: Z → log(REER) (no LFP) | log_gdp_pc | 0.0537 | 0.0149 | 0.0003 | *** |
| C3: Z → log(REER) (no LFP) | rgdp_growth | -0.0003 | 0.0003 | 0.2582 |  |
| C4: Z → log(REER) + LFP | Z_1 | -1.3278 | 0.3974 | 0.0008 | *** |
| C4: Z → log(REER) + LFP | Z_2 | 0.1742 | 0.0578 | 0.0026 | *** |
| C4: Z → log(REER) + LFP | Z_3 | -0.0065 | 0.0023 | 0.0050 | *** |
| C4: Z → log(REER) + LFP | lfp_rate | 0.0005 | 0.0010 | 0.5783 |  |
| C4: Z → log(REER) + LFP | log_gdp_pc | 0.0542 | 0.0152 | 0.0004 | *** |
| C4: Z → log(REER) + LFP | rgdp_growth | -0.0002 | 0.0003 | 0.3561 |  |
| C5: Z → GDP growth | Z_1 | -1.7452 | 4.7185 | 0.7115 |  |
| C5: Z → GDP growth | Z_2 | 0.3187 | 0.6972 | 0.6476 |  |
| C5: Z → GDP growth | Z_3 | -0.0176 | 0.0281 | 0.5327 |  |
| C5: Z → GDP growth | log_gdp_pc | 0.2642 | 0.1742 | 0.1295 |  |
| C6: Z → log(REER) (no growth) | Z_1 | -1.2026 | 0.3761 | 0.0014 | *** |
| C6: Z → log(REER) (no growth) | Z_2 | 0.1550 | 0.0545 | 0.0045 | *** |
| C6: Z → log(REER) (no growth) | Z_3 | -0.0057 | 0.0022 | 0.0088 | *** |
| C6: Z → log(REER) (no growth) | log_gdp_pc | 0.0501 | 0.0146 | 0.0006 | *** |
| C7: Z + working_age_share | Z_1 | -0.5911 | 0.5453 | 0.2785 |  |
| C7: Z + working_age_share | Z_2 | 0.1028 | 0.0638 | 0.1075 |  |
| C7: Z + working_age_share | Z_3 | -0.0046 | 0.0023 | 0.0438 | ** |
| C7: Z + working_age_share | working_age_share | -1.1678 | 0.7495 | 0.1193 |  |
| C7: Z + working_age_share | log_gdp_pc | 0.0535 | 0.0148 | 0.0003 | *** |
| C7: Z + working_age_share | rgdp_growth | -0.0003 | 0.0003 | 0.2838 |  |

*Z₁ attenuation when adding LFP: -1.2092 → -1.3278 (-9.8%)*

*Mechanism chain: Demographics → labor supply (LFP) → relative productivity → REER*